10.5.46 Conformal mappings

Problem: Construct a linear-fractional function that maps the points \( z_{1}, z_{2}, z_{3} \) corresponding to the points \( w_{1}, w_{2}, w_{3} \). \[ z_{1}=3, z_{2}=2, z_{3}=3 i, w_{1}=1+i, w_{2}=0, w_{3}=\infty . \]